The purpose of this project is to develop theory for the interpretation of biomedical and chemical measurement techniques. At present we are working on optical spectroscopy applied to estimate optical tissue parameters to distinguish between normal and abnormal tissues. The project deals with the theory of optical measurements as used to estimate optical properties of human tissue. This project has generated research on defining the region of tissue visited by laser-generated photons. Since it has been shown that properties of tissue can successfully be found from models based on random walks on discrete lattices, we have identified the region visited by photons with the expected number of distinct sites visited by the random walk conditioned to emerge at an interface, where it can be identified with a light intensity. A physical model has been developed for this process and applied to reflectance and transillumination measurements. With regard to the use of optical techniques for imaging purposes we have proposed a technique for characterizing the region probed by a photon which is ultimately re-emitted by the medium (i.e., tissue). This is based on the observation that tissue can be modeled as a simple cubic lattice. It is possible to calculate the expected number of lattice sites visited by a re-emitted photon. This then provides a parameter related to the region visited by the photon. A more recent project relates to developing theory to treat photon migration in tissues, exemplified by teeth, in which the underlying optical parameters are anisotropic. As a first step we have considered a very specific form of anisotropy which allows two favored directions, but a theory to deal with more general forms of anisotripicity is currently being developed.